Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I have a table T with 10 numbers .How can I plot this table ?

Thanks for any explanation !

'Export as pdf' is not one of the  'Export as' options on  a Mac. Instead, you should follow these instructions, from

?pdf:

 
1. Open the worksheet that you want to export.
2. From the File menu, select Print.
3. Specify options for export to PDF as described in Section Options for Export to PDF below.
4. From the PDF drop-down list, select Save as PDF...
5. In the Save As dialog, enter a filename.
Click Save.

 

I am trying  to solve a first order differential equation.  But the maple is not able to solve. Please help me in finding the solutions...

Exact solution is not necessary. Solution in the series expansion is also be very helpful.

Here is the attached maple code..Please do check. Please scroll down to download the given maple file.


 

``

``

restart

with(Student[NumericalAnalysis])

with(PDEtools)

with(DEtools)

with(MmaTranslator)

[FromMma, FromMmaNotebook, Mma, MmaToMaple]

(1)

``

``

``

C1 := 2*M/(4*M*R^2*a-3*R^3*a)

``

D1 := -M*(8*M-9*R)*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(3*R^2*(-16*M^2+26*M*R-9*R^2+(16*M^2-30*M*R+11*R^2)*ln(1+2*M/(4*M-3*R))+R^2*ln(-3*R/(4*M-3*R))))

``

A1 := R^2*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(-32*M^2+52*M*R-18*R^2+(2*(16*M^2-30*M*R+11*R^2))*ln(1+2*M/(4*M-3*R))+2*R^2*ln(-3*R/(4*M-3*R)))

``

explambda := simplify((-2*C1*a*r^2+1)/(C1*a*r^2+1))

``

density := simplify(a*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

pr := simplify(-D1+3*a*A1*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

pt := simplify((D1*(-D1*r^2+4)-4*a^4*C1^4*r^6*(9*(1+A1)^2-(4*(1+3*A1))*D1*r^2+4*D1^2*r^4)+2*a*C1*(18*A1-(16+9*A1)*D1*r^2+4*D1^2*r^4)-3*a^2*C1^2*r^2*(9+16*A1+27*A1^2-(28*(1+A1))*D1*r^2+8*D1^2*r^4)+4*a^3*C1^3*r^4*(18+3*A1*(17+9*A1)-(10*(2+3*A1))*D1*r^2+8*D1^2*r^4))/((4*(C1*a*r^2+1))*(2*C1*a*r^2-1)^3))

``

drhodp := simplify(1/A1)

``

dptdp := (diff(pt, r))/(diff(pr, r))

``

A := simplify(-(-1-explambda)/r+4*explambda*Pi*r*(pr-density))

``

B := -(explambda^2+4*explambda+1)/r^2-64*explambda^2*Pi^2*r^2*pr^2-16*explambda*Pi*((-2+explambda)*pr-pt-density)-(-4*explambda*Pi*(pr+density)-4*explambda*Pi*drhodp*(pr+density))/dptdp

``

sys := {r*(diff(y(r), r))+y(r)^2+(A*r-1)*y(r)+r^2*B = 0}

 

[moderator edited to remove pages of output]
 

Download CALCULATION_OF_Y_v1.mw
 

Hi!

Are there any plans to release a native Maple version for the Apple silicone (ARM architecture) Macs? I suppose that the current versions will work fine through Rosetta 2 emulation layer, but the Rosetta 2 will be removed from Mac OS in 2-3 years. Moreover, the native app would be much faster.

Thank you  

Good morning,

I'm new to Maple and have an informal learning relationship with calculus.

I'm exploring an expression but want the max value of a variable to be based on another equation. 

I'd be curious how to do this and then how to also graph and table the exploration. 

I'd like to evaluate, graph, and table this:

s = u*t + 1/2*a*t^2

Where the maximum value of t = (v - u)/a

s = distace

u = starting velocity

v = final velocity

a = acceleration

t = time for acceleration to reach final velocity

Thank you.

I am testing Maple 2020.2 with new Latex with Physics version latest 879.

The latex generated now issues \! between the symbol and the () next to it to improve the spacing. This post is just to let anyone using the package mleftright in Latex, that this will cause a problem. So it is better to remove this package if you are allready using it.

Here is an example

eq:=y(x)=exp(x/2);
Latex(eq)

              y \! \left(x \right) = {\mathrm e}^{\frac{x}{2}}

In earlier version of Physics:-Latex (now it is just Latex), the above generated this

             y  \left(x \right) = {\mathrm e}^{\frac{x}{2}}

Notice, no \! in earlier version.

If you happen to be using \usepackage{mleftright} to improve the spacing for \left and \right, which I was using, you'll get negative side effect. A solution is to remove this package. Here is an example showing the above Latex compiled with this package added, and without it, so you can see the differerence.

\documentclass[12pt]{book}
\usepackage{amsmath} 
\usepackage{mleftright}
\mleftright
\begin{document}

With the package mleftright loaded

which gives using latest Latex V 879. Maple 2020.2
\[
  y \! \left(x \right) = {\mathrm e}^{\frac{x}{2}}
\]
            
And which gives using earlier Physics Latex. Using Maple 2020.1
\[
  y \left(x \right) = {\mathrm e}^{\frac{x}{2}}
\]
\end{document}

This is the output without using this package. by removing the inlcude command in the above Latex code and not calling mlfright. Now the problem is gone:

I like the effect added from \! , which is a manual way to improve the space, which this package was doing.

just be careful not to use mleftright package now, which is a somewhat popular package in latex and It was recommended to use sometime ago to improve the spacing, as it will over correct the spacing, and looks like not needed any more with latest Maple Latex.

 

 

How to write the differential equation only according to the graph? Is the temperature related to newton's cooling law? 

Quite confused about this graph. 

Anyone can help me? Thank you so much! 

I cannot install the latest physics update 877 even after installing 2020.2 update. Geting an error message will try to attach screen shot. Update worked fine on physics update yesterday. Maple 2020.2 on MacBookPro OS 10.15.7

Don't know how to attach screen shot so here is text from install window;

Fetching package "Physics Updates" from MapleCloud...
ID: 5137472255164416
Version: 877
URL: https://maple.cloud

An error occurred, the package was not installed: 
Could not open workbook: /private/var/folders/bb/1n47nzcx18v_l2wy573v7z0c0000gn/T/cloudDownload5932106080613470167/Physics+Updates.maple

Tried at least 3 times before 2020.2 update and 2 times after. Similar results (diiferent download numbers each time).

Is there any useful preprocessing -- or a better data structure -- for efficient set membership testing?

I have a list X of 1.5 million hashes (30-digit compressions of arrays) and want to find an element which belongs to both this set and another set. The other set Y has 270 billion elements so I will generate just a fraction of these (a sample size of a few hundred million should be enough to give a collision). Will membership testing be faster if I first sort X? Or is the sort operation too expensive to see any visible benefit?

I have the equation x^4=4(4x^2-y^2), and I keyed in maple

>with (plots):
>eq:=x^4=4*(4*x^2-y^2);

and recieve in response x^4=4. 

I want to get eq:=x^4=4(4x^2-y^2), in order to find and graph all possible tangents in the event that y=3 and to find the point of intersection for the tangents that lie in the first quadrant. 

Thanks 

 

how this integro-differential equation can be solved?
any assumption or suggestion is appreciated. tnx in advance

EDITED: parameters are added.


 

restart

w[c]:=0.01:delta:=5:Omega:=5:w[0]:=1:gamma_0:=1:k[b]:=1:T:=100:nu[n]:=2*Pi*n*k[b]*T;

200*Pi*n

(1)

F:=2*gamma_0*w[c]^2*exp(-w[c]*tau)*sin(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau):

k1:=2*k[b]*T*w[c]^2*sum((w[c]*exp(-w[c]*tau)-abs(nu[n])*exp(-abs(nu[n])*tau))/(w[c]^2-nu[n]^2),n=-infinity..infinity):

G:=cos(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau)*k1:

eq:=diff(rho(t),t)+Int(G*rho(tau),tau=0..t)=1/2*Int(G-F,tau=0..t);

diff(rho(t), t)+Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))*rho(tau), tau = 0 .. t) = (1/2)*(Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))-0.2e-3*exp(-0.1e-1*tau)*sin(sin(5*t)-sin(5*t-5*tau)+tau), tau = 0 .. t))

(2)

 


 

Download integro.mw

Is it possible to draw a graph without names for the vertices? I would get something like this.

The worksheet below is a failed attempt to produce the display of a pencil of conics tangent to four lines. The worksheet contains an image of the display.

Comments within the worksheet describe the details of the attempt and the solve command which fails.

dhaar provided an answer to a similar question which I posed on November 12 (its web address is in the worksheet) and I hope s(he) will reply to this one as well.

ConicsTangent.mw

 

Hello there, 

Would you allow me to ask this question?

What would be a way to make the 'expression' as 'expression_desired' below?

In other words, what would be a way to cancel I (or j) and exp(-pi/2) each other?


 

restart;

expression := exp(-I/2*(-2*rho__m + pi))*I;

I*exp(-((1/2)*I)*(-2*rho__m+pi))

(1)

expression_desired := exp(I*(rho__m));

 

exp(I*rho__m)

(2)

 


Thank you, 

Download Q20201118.mw

I  installed Maple 2020 a week ago.   When I try to update the Maple Physics Package, the installation stalls.

Output to the command  Physics:-Version(latest):

`The "Physics Updates" version "872" is installed but is not active. The active version of Physics is within the library C:\\Program Files\\Maple 2020\\lib\\maple.mla, created 2020, March 4, 19:36 hours`

I note that there was similar complaint in June.  I am surprised that this has not yet been fixed. The reply in June seemed to be do a manual update, but I am unclear how to do that.   I can download the latest package, but I do not know how to  (or where) to install this package.  Do I just delete the version in C:\\Program Files\\Maple 2020\\lib\\maple.mla and paste the new version?

I would greatly appreciate any help since the main reason I purchased the new Maple 2020 was to use the most recent versions of the Physics package.

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